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# Charles' Law

## Calculating the relationship between volume and temperature of a gas.

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Charles' Law

In the 1700s and 1800s, hot air balloons were very popular. Why wouldn’t they be? Riding in a hot air balloon allowed people to travel through the air and get a bird’s eye view of the landscape at a time when airplanes did not yet exist. Do you know why hot air can inflate a balloon? Read on to find out.

### Up, Up, and Away

The popularity of hot air balloons got scientists thinking about gases and what happens to them when they heat up. In the early 1800s, two French scientists—Jacques Charles and Joseph Gay-Lussac—decided to investigate how changes in the temperature of a gas affect the amount of space it takes up, or its volume. They heated air and measured how its volume changed. The two scientists already knew that the pressure of a gas affects it volume. This had been demonstrated back in the 1660s by the English scientist Robert Boyle. So Charles and Gay-Lussac controlled the effects of pressure by keeping it constant in their experiments.

Based on the results of the research, Charles developed a scientific law about gases. It is one of three well-known gas laws, the others being Boyle’s law and Amontons’ law. According to Charles’ law, when the pressure of a gas is held constant, increasing its temperature increases its volume. The opposite is also true: decreasing the temperature of a gas decreases it volume.

### You Try It!

At the URL below, you can simulate Charles’ and Gay-Lussac’s work. The simulation lets you choose different temperatures for a gas and see how it affects the volume of the gas. After you have recorded several sets of values in the data table, use the graphing feature to plot the points.

http://group.chem.iastate.edu/Greenbowe/sections/projectfolder/flashfiles/gaslaw/charles_law.html

Q: What does the graph of the data look like?

A: The graph is a straight line that rises from left to right. This type of graph shows that both variables increase together at a constant rate.

Q: Could you use the graph to find the volume of a gas at a temperature you didn’t choose for your data table?

A: Yes, you could. You could find the temperature on the temperature scale, trace straight up from this point to the graph line, and then trace straight across to the volume scale to find the volume for that temperature.

### Amazing Motion

Can you guess why the volume of a gas increases when it is heated? Heating a gas gives its particles more energy. With more energy, the particles move faster. You can see this in the simulation at the URL below. Drag the bar to increase the temperature, and you’ll be amazed at how fast the particles zigzag around inside the box! If the speedy particles had more room, they would spread out and the volume of the gas would increase.

Q: Now that you know how a gas behaves when it is heated, can you explain how hot air causes a balloon to inflate?

A: As the air heats, its particles spread out and occupy more space, causing the balloon to inflate.

### Summary

• According to Charles’ law, when the pressure of a gas is held constant, increasing its temperature increases its volume.
• Heating a gas gives its particles more energy so they move faster. If the speedy particles have room to spread out, the volume of the gas will increase.

### Explore More

Do the activity on Charles’ law at the following URL. Be sure to answer the questions at the end of the activity.

http://www.wisc-online.com/objects/ViewObject.aspx?ID=HYP4107

### Review

1. State how increasing the temperature of a gas changes its volume, assuming pressure is held constant.
2. With the help of his dad, a boy in the Figure below blew up a bunch of balloons outside on a hot, sunny day. The outdoor temperature was 26°C. Then the boy took the balloons inside his air-conditioned house, where the temperature was 20°C. What do you think happened to the balloons after they had been inside the cool house for a while? Explain.

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